Abstract
The state of a neuron is described by the neuron potential (NP), which often has the nature of a stochastic process.
In this paper, the stochastic information processes of the spontaneous type neuron and the forced type neuron are discussed through the density of the first passage time when the NP reaches the threshold, and its subsidiary statistical quantity, the transition probability density function. These quantities can be obtained from Kolmogorov's equation and the law of probability conservation. However, the analytical solution is obtainable only in very simple cases. Hence, we took the position of obtaining these quantities by means of numerical analysis and investigating some rather complex properties of the neurons. Accordingly, we could discuss the varying threshold problem and the case when input pulse trains carry the PFM information.
And in the case of the periodic PFM, the output spike interval density becomes the important quantity because it is measured in practice. Therefore we clarified its relationship to the first passage time density and then presented the method of approximation.
